# A Graph Neural Network Framework for Grid-Based Simulation

arXiv: https://arxiv.org/abs/2202.02652 · HTML: https://mlsanity.com/paper/2202.02652/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 4 references that are in the map.
- First posted on arXiv 5 Feb 2022.

## Builds on (most cited first, 4 of 4)

- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Use of low-fidelity models with machine-learning error correction for well placement optimization](https://mlsanity.com/paper/2111.02960/) (2021)

## Abstract (arXiv)

Reservoir simulations are computationally expensive in the well control and well placement optimization. Generally, numerous simulation runs (realizations) are needed in order to achieve the optimal well locations. In this paper, we propose a graph neural network (GNN) framework to build a surrogate feed-forward model which replaces simulation runs to accelerate the optimization process. Our GNN framework includes an encoder, a process, and a decoder which takes input from the processed graph data designed and generated from the simulation raw data. We train the GNN model with 6000 samples (equivalent to 40 well configurations) with each containing the previous step state variable and the next step state variable. We test the GNN model with another 6000 samples and after model tuning, both one-step prediction and rollout prediction achieve a close match with the simulation results. Our GNN framework shows great potential in the application of well-related subsurface optimization including oil and gas as well as carbon capture sequestration (CCS).